Let (V, ω) be an orthosymplectic ℤ₂-graded vector space and let 𝔤:= 𝔤𝔬𝔰𝔭 (V, ω) denote the Lie superalgebra of similitudes of (V, ω). It is known that as a 𝔤-module, the space

We also transcend our results on the eigenvalues of Capelli operators to the Deligne category Rep (O_t). More precisely, we define categorical Capelli operators \( {\left\{{D}_{t,\leftthreetimes}\right\}}_{\leftthreetimes \in \mathcal{T}} \) that induce morphisms of indecomposable components of symmetric powers of V_t, where V_t is the generating object of Rep (O_t). We obtain formulas for the eigenvalue polynomials associated to the \( {\left\{{D}_{t,\leftthreetimes}\right\}}_{\leftthreetimes \in \mathcal{T}} \) that are analogous to our results for the operators \( {\left\{{D}_{\leftthreetimes}\right\}}_{\leftthreetimes \in \mathcal{T}} \).

设（V，ω）是orthosymplecticℤ ₂ -graded矢量空间和让𝔤：=𝔤𝔬𝔰𝔭（V，ω）表示的（similitudes的李代数V，ω）。众所周知，空间是𝔤模块

我们还将Capelli算子的特征值的结果超越到Deligne类别Rep（O _t）。更精确地，我们定义分类卡佩里运营商\（{\左\ {{d} _ {T，\ leftthreetimes} \右\}} _ {\ leftthreetimes \在\ mathcal【T}} \）诱导不可分解部件的态射的对称幂V _t，其中V _t是Rep（O _t）的生成对象。我们获得与\（{\ left \ {{D} _ {t，\ leftthreetimes} \ right \}} _ {\ leftthreetimes \ in \ mathcal {T}} \）相关的特征值多项式的公式类似于我们为运营商提供的结果\（{\ left \ {{D} _ {\ leftthreetimes} \ right \}} _ {\ leftthreetimes \ in \ mathcal {T}} \\）。